This textbook is a thorough accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear coherent illustrations Digital Fourier Analysis includes practice problems and thorough Appendices for the advanced reader. As a special feature the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively allowing the user to experiment with the underlying mathematics. For example a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency the reader can test various cases and view the results until they fully understand the principle. Additionally the applet source code in Visual Basic is provided online allowing this book to be used for teaching simple programming techniques. A complete intuitive guide to the basics Digital Fourier Analysis - Fundamentals is an essential reference for undergraduate students in science and engineering.